It is known that the achievement of a variable valve lift of the gas-exchange valve of internal combustion engines has a critical influence on the operating behavior and operating values of an internal combustion engine. DE 42 23 172 C1 discloses a device, in which, to achieve a variable valve lift from a cam of a camshaft, a moved rocker lever is guided in a long hole on a bolt fixed to the housing. The movement of the rocker lever in the long hole is in this case dependent on the position of the eccentric shaft. In general, to achieve a variable valve control, inter alia, known four-member valve mechanisms allow a continuous variation in the valve-lift profile when the internal combustion engine is in operation. A four-member valve mechanism of this type is described in U.S. Pat. No. 5,303,759, corresponding to DE 38 33 540 C2, and DE 43 22 449 A1 by means of a device for the actuation of the valves on internal combustion engines with a variable valve elevation curve. This device, according to U.S. Pat. No. 5,303,759, consists of a guide member acting at the same time as an output member which transmits the movement of an intermediate member to the valve or to the valve stem, the intermediate member being supported on the housing via a curved joint, and the curve, arranged on the intermediate member, of this curved joint having a catch-forming portion and a control portion, and the position of the curve belonging to this curved joint and supported on the housing or the position of the rotary joint of the cam being adjustable during operation. By contrast, in the device according to DE 43 22 449 A1, the intermediate member is additionally supported via a fourth curved joint, in order to define the paths of movement of the intermediate member unequivocally. U.S. Pat. No. 5,303,759, which also corresponds to EP 03 89 609 B1, discloses a further device for actuating the valve on internal combustion engines with a variable valve elevation curve, in which the joint between the intermediate member and the output member is designed as a rotary joint and the joint between the output member and the housing is designed as a sliding joint.